What is the difference between the interest rate and the APR?

The interest rate prices the borrowing; the APR prices the borrowing plus the fees, expressed as an annual rate on the money you actually received. Two loans at the same rate can have very different APRs.

Why do fees hurt more on a short loan?

Because the same fee is spread over fewer payments. 3% of fees adds about 0.2 points to the APR on a 30-year mortgage and about 1.4 points on a five-year car loan.

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APR Calculator

The APR is the rate that makes the money you actually receive equal the payments you actually make. Fees deducted up front raise it above the quoted rate, sometimes considerably.

Also called: annual percentage rate calculator, effective loan rate.

APR

7.1%

The nominal rate is 6.9%, but once $5,000 of up-front fees are counted the APR is 7.1%. You receive $245,000.00 and repay $1,646.50 a month.

Monthly instalment

$1,646.50

Amount actually advanced

$245,000.00

How much the fees add

0.2%

Total cost including fees

$347,740.00

How this is calculated

An estimate, not an offer or a guarantee. Projected returns assume the rate you entered holds for the whole term, which no market does.

Method and background

This is what the calculation gives for the numbers you entered. It is an estimate, not advice, and it knows nothing about your situation beyond those numbers. Rules for United States change on a published schedule; the effective date is shown on every rule-based tool.

How this is calculated

The instalment is calculated on the full loan amount, but you only receive the amount net of fees. The APR is the rate at which the net advance amortises to that same instalment. Because the numerator shrank and the payment did not, the APR is always at or above the nominal rate.

solve for i: (P - F) * i(1+i)^n / ((1+i)^n - 1) = E, where E is computed on the full P

F: Fees deducted from the advance (currency)
i: Periodic APR (decimal)

Full derivation: Why an 8% flat loan is really a 14.13% loan

Worked examples

Each of these is asserted on every build. If a change to the engine ever moved one of these answers, the build would fail before the page could print it.

5k of fees on a 250k 30-year loan

Loan amount: $250,000.00
Nominal interest rate: 6.9%
Tenure: 30 years
Fees paid up front: $5,000.00

APR7.1%

independent bisection on the net advance of 245,000 against a payment of 1,646.50

Open this example

fees on a short term hurt much more

Loan amount: $25,000.00
Nominal interest rate: 8.5%
Tenure: 5 years
Fees paid up front: $800.00

APR9.894%

independent bisection: PMT(8.5%/12, 60, -25000) = 512.91 against a net advance of 24,200 solves to 9.89%. The same 3.2% of fees spread over 60 months rather than 360 costs 1.39 points instead of a fifth of that.

Open this example

no fees means APR equals the nominal rate

Loan amount: $250,000.00
Nominal interest rate: 6.9%
Tenure: 30 years
Fees paid up front: $0.00

APR6.9%

degenerate case: with no fees the two definitions must coincide

Open this example

Method and limits

What it assumes

All fees are paid at drawdown and financed from the advance.

What it deliberately does not model

Regulatory APR definitions differ between markets in which fees must be included. This computes the economic APR on the fees you enter.

Formula version 1.0.0 · definition 1.0.0 · United States · Report a problem with this calculator

Frequently asked questions

What is the difference between the interest rate and the APR?: The interest rate prices the borrowing; the APR prices the borrowing plus the fees, expressed as an annual rate on the money you actually received. Two loans at the same rate can have very different APRs.
Why do fees hurt more on a short loan?: Because the same fee is spread over fewer payments. 3% of fees adds about 0.2 points to the APR on a 30-year mortgage and about 1.4 points on a five-year car loan.